Rotational Ligand Dynamics in Mn[N(CN) 2 ] 2 .pyrazine

1. Rotational Ligand Dynamics in Mn[N(CN)2]2.pyrazine Craig Brown, John Copley Inma Peral and Yiming Qiu NIST Summer School 2003

2. Outline • Mn[N(CN)2]2.pyrazine • Physical Properties • Review data from other techniques • Compare behaviour with related compounds • Quasi-elastic scattering • What is it? • What it means • How TOF works and what we measure • Categories of experiments performed on DCS

3. Pyrazine N H/D C

4. Complex number real scattering imaginaryabsorption Coherent scattering Incoherent scattering Depends on the mean square difference scattering length Depends on the average scattering length STRUCTURE DYNAMICS Interactions The neutron-nucleus interaction is described by a scattering length

5. Structure and dynamics • Deuteratedsample for coherent Bragg diffraction to obtain structure as a function of temperature • Protonatedto observe both single particle motion (quasielastic) and to weigh the inelastic scattering spectrum in favor of hydrogen (vibrations) • Deuterationcan help to assignparticular vibrational modes and provide a ‘correction’to the quasielastic data for the paramagnetic scattering of manganese and coherent quasielastic scattering.

6. BT1 l=1.54 Å HMI l=2.448 Å Magnetic Structure • One of the interpenetrating lattices shown. • a is up, b across, c into page • Magnetic cell is (½, 0, ½) superstructure • Exchange along Mn-pyz-Mn chain 40x J. L. Manson et. al J. Am. Chem. Soc. 2000 J. Magn. Mag. Mats. 2003

7. Mn[N(CN)2]2.pyrazine

8. 1.3 K ~200 K Lose pyz 408 K Phase transition Mn[N(CN)2]2.pyrazine • 3-D antiferromagnetic order below ~2.5 K • Magnetic moments aligned along ac (4.2 mB) • Monoclinic lattice (a=7.3 Å, b=16.7 Å, c=8.8 Å) • Phase transition to orthorhombic structure • Large Debye-Waller factor on dicyanamide ligand • Diffuse scattering • Phase transition • Large Debye-Waller factors • on pyrazine ~435 K • Decomposes and loses pyrazine.

9. As a function of Temperature

10. The other compounds • MnCl2.pyz • Cu[N(CN)2]2.pyz

11. AIMS • Experience Practical QENS • sample choice • geometry consideration • Learn something about the instrument • Wavelength / Resolution / Intensity • Data Reduction • Data Analysis and Interpretation • instrument resolution function and fitting • extract EISF and linewidth • spatial and temporal information

12. The Measured Scattering

13. Quasielastic Scattering • The intensity of the scattered neutron is broadly distributed about zero energy transfer to the sample • Lineshape is often Lorentzian-like • Arises from atomic motion that is • Diffusive • Reorientational • The instrumental resolution determines the timescales observable • The Q-range determines the spatial properties that are observable • (The complexity of the motion(s) can make interpretation difficult)

14. The Measured Scattering Instrumental resolution function The reorientational and/or Lattice parts. The Lattice part has little effect in the QE region- a flat background (see Bée, pp. 66) Debye-Waller factor Far away from the QE region Quasielastic Neutron Scattering Principles and applications in Solid State Chemistry, Biology and Materials Science M. Bee (Adam Hilger 1988)

15. Quasielastic Scattering Gs(r,t) is the probability that a particle be at r at time t, given that it was at the origin at time t=0 (self-pair correlation function) Iinc(Q,t) is the space Fourier transform of Gs(r,t) (incoherent intermediate scattering function) Sinc(Q,w) is the time Fourier transform of Is(Q,t) (incoherent scattering law)

16. Quasielastic Scattering r1 r2 Jump model between two equivalent sites

17. Powder (spherical) average EISF!!!!!!!!!! QISF!!!!!!!!! Quasielastic Scattering r1 r2 Jump model between two equivalent sites

18. Quasielastic Scattering r1 r2 Jump model between two equivalent sites Aod(w) Half Width ~1/t (independent of Q) w 0

19. Width EISF Ao = ½[1+sin(2Qr)/(2Qr)] 1 ½ Q Qr Quasielastic Scattering Jump model between two equivalent sites

20. Quasielastic Scattering Jumps between three equivalent sites

21. Width Q2 Quasielastic Scattering Translational Diffusion

22. Dps t=ts v=vi Sample 2q Pulser Monochromator v=vf t=0 Detector Dsd t=tD detector sample pulsed mono TOF spectroscopy, in principle

23. TOF spectroscopy, in practice (1) The neutron guide (2) The choppers (3) The sample area (4) The flight chamber and the detectors

24. Types of Experiments • Translational and rotational diffusion processes, where scattering experiments provide information about time scales, length scales and geometrical constraints; the ability to access a wide range of wave vector transfers, with good energy resolution, is key to the success of such investigations • Low energy vibrational and magnetic excitations and densities of states • Tunneling phenomena • Chemistry--- e.g. clathrates, molecular crystals, fullerenes • Polymers --- bound polymers, glass phenomenon, confinement effects • Biological systems--- protein folding, protein preservation, water dynamics in membranes • Physics --- adsorbate dynamics in mesoporous systems (zeolites and clays) and in confined geometries, metal-hydrogen systems, glasses, magnetic systems • Materials--- negative thermal expansion materials, low conductivity materials, hydration of cement, carbon nanotubes, proton conductors, metal hydrides